Project Summary/Abstract Mathematical cognition provides a foundation for the development of quantitative skills critical for functioning in the 21st century. Yet, math difficulties are widespread in children, adolescents, and college students, and one in five adults in the USA is functionally innumerate. Low numeracy is associated with poorer health outcomes, reduced health literacy, and improper use of health resources. Characterizing neurocognitive developmental trajectories and risk factors of mathematical disabilities (MD) is critical for addressing the public health burdens of innumeracy. Building on an innovative and high-impact line of research, we propose to investigate neurocognitive longitudinal trajectories and outcomes in MD. We focus on two key cognitive domains impaired in MD: (1) number sense, including representations of quantities, numbers, and their mental manipulation, and (2) arithmetic skills, including numerical problem solving and fluent retrieval of math facts from memory. Our central hypothesis is that, relative to typically developing (TD) controls, individuals with MD will exhibit atypical developmental trajectories of brain response, representations, and connectivity in two functional brain systems: (1) the parietal visuo-spatial attention system, which supports quantity representations, and (2) the medial temporal (MTL) declarative memory system, which supports arithmetic fact retrieval. We will test (1) core and access deficit models of atypical number sense development and (2) a memory deficit model of weak fact retrieval. Using state-of-the-art multimodal brain imaging and three innovative longitudinal designs, we will test these models by (1) characterizing developmental trajectories in children and adolescents, spanning elementary, middle, and high school years (ages 7 to 16), with an accelerated longitudinal design; (2) identify brain measures that predict longitudinal 2-year early math trajectories and outcomes in young children prior to formal instruction or MD diagnosis (ages 5-7); and (3) identify brain measures that predict longitudinal 10-year long-term math outcomes in adolescents (age 17) who were previously characterized in childhood. Three innovative longitudinal designs will address critical gaps in our understanding of neurocognitive systems impacted over development in MD. Findings will inform our understanding of the etiology of MD and the development of targeted cognitive interventions that may ultimately reduce the public health burden of low numeracy.